Inflationary solutions in the brane world and their geometrical interpretation - art. no. 103505

We consider the cosmology of a pair of domain walls bounding a five-dimensi onal bulk space-time with a negative cosmological constant, in which the di stance between the branes is not fixed in time. Although there are strong a rguments to suggest that this distance should be stabilized in the present epoch, no such constraints exist for the early universe and thus non-static solutions might provide relevant inflationary scenarios. We find the gener al solution for the standard ansatz where the bulk is foliated by planar-sy mmetric hypersurfaces. We show that in all cases the bulk geometry is that of anti-de Sitter (AdS(5)) space. We then present a geometrical interpretat ion for the solutions as embeddings of two de Sitter (dS(4)) surfaces in Ad S(5), which provide a simple interpretation of the physical properties of t he solutions. A notable feature explained in the analysis is that two-way c ommunication between branes expanding away from one another is possible for a finite amount of time, after which communication can proceed in one dire ction only. The geometrical picture also shows that our class of solutions (and related solutions in the literature) is not completely general, contra ry to some claims. We then derive the most general solution for two walls i n AdS(5). This includes novel cosmologies where the brane tensions are not constrained to have opposite signs. The construction naturally generalizes to arbitrary FRW cosmologies on the branes.